186 
MINUTES OF PROCEEDINGS OF 
connected with s by an equation of the form t—as+bs' 2 . This would give the 
velocity v at that point = [a 4- 2 Is)- 1 , and a retarding force varying as v z . 
If the average values of s and t, determined by experiment at the 4th and 
8th screens, be used to find a and b, we have 
*31845 = a X 360 + b X (360) 2 , 
*75988 = a x 840 + b x (840) 2 , 
which two equations give a = *000, 869, 558, 
b = *000, 000, 0417, 
and .*. £ = *000, 869, 558 s + *000, 000, 0417 s 3 , 
1006 
V *869, 558, + -000,0834s* 
Or if we measure the distance s' from the gun we have s^s + 120 or s=s'—120, 
1000 
* *869, 588 + '000,0834 {s' - 120) 
1000 
“ -859, 550 +-000, 0834s'’ 
and giving s r the particular values 0, 100, 200, &c., we find the velocities of 
the shot at 0, 100, 200, &c. feet from the gun by the formula, which we 
may compare with those derived purely from experiment by interpolation, as 
given above 
Distance 
from gun. 
Velocity by 
Formula. 
Difference. 
Velocity by 
Experiment. 
ft. 
f.s. 
f.s. 
f.s. 
0 
1163-4 
* * * 
100 
1152-2 
* 
# # # 
200 
1141-3 
o-o 
1141-3 
300 
1130-5 
-0-3 
1130-2 
400 
1119-9 
-0-5 
1119-4 
500 
1109-6 
-0-8 
1108-8 
600 
1099-4 
-0-7 
1098-7 
700 
1089-4 
-0-4 
1089-0 
800 
1079-6 
0-0 
1079-6 
900 
1070-0 
+ 0-5 
1070-5 
1000 
1060-5 
+ 1-2 
1061-7 
It is evident that this table requires to be extended both ways, so as to give 
the law for higher and lower velocities. Thus initial velocities of 1200 f.s. 
or more, and lower velocities of 1100, 1050, 1000 f.s., &c., are required. 
In all these cases it must be remembered that our velocity is the horizontal 
dx . . 
velocity ^ or v L of M. Didion. 
To obtain a satisfactory table shewing the velocity of a given ball pro¬ 
jected with the highest possible velocity, at all distances from the gun, I am 
satisfied that four good shots through ten screens with each particular charge 
would be amply sufficient. The shot should have exactly the same form of head* 
